Colloidal crystal

A colloidal crystal is an ordered array of colloid particles, analogous to a standard crystal whose repeating subunits are atoms or molecules.[1] A natural example of this phenomenon can be found in the gem opal, where spheres of silica assume a close-packed locally periodic structure under moderate compression.[2] Bulk properties of a colloidal crystal depend on composition, particle size, packing arrangement, and degree of regularity. Applications include photonics, materials processing, and the study of self-assembly and phase transitions.

Introduction

A colloidal crystal is a highly ordered array of particles which can be formed over a long range (to about a centimeter). Arrays such as this appear to be analogous to their atomic or molecular counterparts with proper scaling considerations. A good natural example of this phenomenon can be found in precious opal, where brilliant regions of pure spectral color result from close-packed domains of colloidal spheres of amorphous silicon dioxide, SiO2 (see above illustration). The spherical particles precipitate in highly siliceous pools and form highly ordered arrays after years of sedimentation and compression under hydrostatic and gravitational forces. The periodic arrays of spherical particles make similar arrays of interstitial voids, which act as a natural diffraction grating for light waves in photonic crystals, especially when the interstitial spacing is of the same order of magnitude as the incident lightwave. [3][4]

Origins
Bulk microstructure of a colloidal crystal composed of submicron amorphous hydrated colloidal silica. The average particle diameter is 600 nm.

The origins of colloidal crystals go back to the mechanical properties of bentonite sols, and the optical properties of Schiller layers in iron oxide sols. The properties are supposed to be due to the ordering of monodisperse inorganic particles.[5] Monodisperse colloids, capable of forming long-range ordered arrays, existing in nature. The discovery by W.M. Stanley of the crystalline forms of the tobacco and tomato viruses provided examples of this. Using X-ray diffraction methods, it was subsequently determined that when concentrated by centrifuging from dilute water suspensions, these virus particles often organized themselves into highly ordered arrays.

Rod-shaped particles in the tobacco mosaic virus could form a two-dimensional triangular lattice, while a body-centered cubic structure was formed from the almost spherical particles in the tomato Bushy Stunt Virus.[6] In 1957, a letter describing the discovery of "A Crystallizable Insect Virus" was published in the journal Nature.[7] Known as the Tipula Iridiscent Virus, from both square and triangular arrays occurring on crystal faces, the authors deduced the face-centered cubic close-packing of virus particles. This type of ordered array has also been observed in cell suspensions, where the symmetry is well adapted to the mode of reproduction of the organism.[8] The limited content of genetic material places a restriction on the size of the protein to be coded by it. The use of a large number of the same proteins to build a protective shell is consistent with the limited length of RNA or DNA content.[9]

It has been known for many years that, due to repulsive Coulombic interactions, electrically charged macromolecules in an aqueous environment can exhibit long-range crystal-like correlations with interparticle separation distances often being considerably greater than the individual particle diameter. In all of the cases in nature, the same iridescence is caused by the diffraction and constructive interference of visible lightwaves which falls under Bragg’s law.

Because of the rarity and pathological properties, neither opal nor any of the organic viruses have been very popular in scientific laboratories. The number of experiments exploring the physics and chemistry of these “colloidal crystals” has emerged as a result of the simple methods which have evolved in 20 years for preparing synthetic monodisperse colloids, both polymer and mineral, and, through various mechanisms, implementing and preserving their long-range order formation.

Trends

Colloidal crystals are receiving increased attention, largely due to their mechanisms of ordering and self-assembly, cooperative motion, structures similar to those observed in condensed matter by both liquids and solids, and structural phase transitions.[10] Phase equilibrium has been considered within the context of their physical similarities, with appropriate scaling, to elastic solids. Observations of the interparticle separation distance has shown a decrease on ordering. This led to a re-evaluation of Langmuir's beliefs about the existence of a long-range attractive component in the interparticle potential.[11]

Colloidal crystals have found application in optics as photonic crystals. Photonics is the science of generating, controlling, and detecting photons (packets of light), particularly in the visible and near Infrared, but also extending to the Ultraviolet, Infrared and far IR portions of the electromagnetic spectrum. The science of photonics includes the emission, transmission, amplification, detection, modulation, and switching of lightwaves over a broad range of frequencies and wavelengths. Photonic devices include electro-optic components such as lasers (Light Amplification by Stimulated Emission of Radiation) and optical fiber. Applications include telecommunications, information processing, illumination, spectroscopy, holography, medicine (surgery, vision correction, endoscopy), military (guided missile) technology, agriculture and robotics.

Polycrystalline colloidal structures have been identified as the basic elements of submicrometre colloidal materials science. [12] Molecular self-assembly has been observed in various biological systems and underlies the formation of a wide variety of complex biological structures. This includes an emerging class of mechanically superior biomaterials based on microstructure features and designs found in nature.

The principal mechanical characteristics and structures of biological ceramics, polymer composites, elastomers, and cellular materials are being re-evaluated, with an emphasis on bioinspired materials and structures. Traditional approaches focus on design methods of biological materials using conventional synthetic materials.[13] The uses have been identified in the synthesis of bioinspired materials through processes that are characteristic of biological systems in nature. This includes the nanoscale self-assembly of the components and the development of hierarchical structures.[14]

Theory and background

Aggregation in colloidal dispersions (or stable suspensions) has been characterized by the degree of interparticle attraction.[15] For attractions strong relative to the thermal energy (given by kT), Brownian motion produces irreversibly flocculated structures with growth rates limited by the rate of particle diffusion. This leads to a description using such parameters as the degree of branching, ramification or fractal dimensionality. A reversible growth model has been constructed by modifying the cluster-cluster aggregation model with a finite inter-particle attraction energy.[16]

In systems where forces of attraction forces are buffered to some degree, a balance of forces leads to an equilibrium phase separation, that is particles coexist with equal chemical potential in two distinct structural phases. The role of the ordered phase as an elastic colloidal solid has been evidenced by the elastic (or reversible) deformation due to the force of gravity. This deformation can be quantified by the distortion of the lattice parameter, or inter-particle spacing.[17]

Periodic ordered lattices behave as linear viscoelastic solids when subjected to small amplitude mechanical deformations. Okano's group experimentally correlated the shear modulus to the frequency of standing shear modes using mechanical resonance techniques in the ultrasonic range (40 to 70 kHz).[18] In oscillatory experiments at lower frequencies (< 40 Hz), the fundamental mode of vibration as well as several higher frequency partial overtones (or harmonics) have been observed. Structurally, most systems exhibit a clear instability toward the formation of periodic domains of relatively short-range order Above a critical amplitude of oscillation, plastic deformation is the primary mode of structural rearrangement.[19]

Equilibrium phase transitions (e.g. order/disorder), an equation of state, and the kinetics of colloidal crystallization have all been actively studied, leading to the development of several methods to control the self-assembly of the colloidal particles.[20] Examples include colloidal epitaxy and space-based reduced-gravity techniques, as well as the use of temperature gradients to define a density gradient.[21] This is somewhat counterintuitive as temperature does not play a role in determining the hard-sphere phase diagram. However, hard-sphere single crystals (size 3 mm) have been obtained from a sample in a concentration regime that would remain in the liquid state in the absence of a temperature gradient.[22]

Using a single colloidal crystal, phonon dispersion of the normal modes of vibration modes were investigated using photon correlation spectroscopy, (or dynamic light scattering. This technique relies on the relaxation or decay of concentration (or density) fluctuations. These are often associated with longitudinal modes in the acoustic range. A distinctive increase in the sound wave velocity (and thus the elastic modulus) by a factor of 2.5 has been observed at the structural transition from colloidal liquid to colloidal solid, or point of ordering.[23][24]

Using a single body-centered cubic colloidal crystal, the occurrence of Kossel lines in diffraction patterns were used to monitor the initial nucleation and subsequent motion caused distortion of the crystal. Continuous or homogeneous deformations occurring beyond the elastic limit produce a 'flowing crystal', where the nucleation site density increases significantly with increasing particle concentration.[25] Lattice dynamics have been investigated for longitudinal as well as transverse modes. The same technique was used to evaluate the crystallization process near the edge of a glass tube. The former might be considered analogous to a homogeneous nucleation event—whereas the latter would clearly be considered a heterogeneous nucleation event, being catalyzed by the surface of the glass tube.

Small-angle laser light scattering has provided information about spatial density fluctuations or the shape of growing crystal grains.[25][26] In addition, confocal laser scanning microscopy has been used to observe crystal growth near a glass surface. Electro-optic shear waves have been induced by an ac pulse, and monitored by reflection spectroscopy as well as light scattering. Kinetics of colloidal crystallization have been measured quantitatively, with nucleation rates being depending on the suspension concentration.[27][28] Similarly, crystal growth rates have been shown to decrease linearly with increasing reciprocal concentration.

Experiments performed in microgravity on the Space Shuttle Columbia suggest that the typical face-centered cubic structure may be induced by gravitational stresses. Crystals tend to exhibit the hcp structure alone (random stacking of hexagonally close-packed crystal planes), in contrast with a mixture of (rhcp) and face-centred cubic packing when allowed sufficient time to reach mechanical equilibrium under gravitational forces on Earth.[29] Glassy (disordered or amorphous)colloidal samples have become fully crystallized in microgravity in less than two weeks.

Two-dimensional (thin film) semi-ordered lattices have been studied using an optical microscope, as well as those collected at electrode surfaces. Digital video microscopy has revealed the existence of an equilibrium hexatic phase as well as a strongly first-order liquid-to-hexatic and hexatic-to-solid phase transition.[30] These observations are in agreement with the explanation that melting might proceed via the unbinding of pairs of lattice dislocations.

Long-range order has been observed in thin films of colloidal liquids under oil—with the faceted edge of an emerging single crystal in alignment with the diffuse streaking pattern in the liquid phase. Structural defects have been directly observed in the ordered solid phase as well as at the interface of the solid and liquid phases. Mobile lattice defects have been observed via Bragg reflections, due to the modulation of the light waves in the strain field of the defect and its stored elastic strain energy.[12][31]

All of the experiments have led to at least one common conclusion: colloidal crystals may indeed mimic their atomic counterparts on appropriate scales of length (spatial) and time (temporal). Defects have been reported to flash by in the blink of an eye in thin films of colloidal crystals under oil using a simple optical (biological) microscope. But quantitatively measuring the rate of its propagation provides an entirely different challenge, which has been measured at somewhere near the speed of sound.

Applications

Photonics

Technologically, colloidal crystals have found application in the world of optics as photonic band gap (PBG) materials (or photonic crystals). Synthetic opals as well as inverse opal configurations are being formed either by natural sedimentation or applied forces, both achieving similar results: long-range ordered structures which provide a natural diffraction grating for lightwaves of wavelength comparable to the particle size.

Novel PBG materials are being formed from opal-semiconductor-polymer composites, typically utilizing the ordered lattice to create an ordered array of holes (or pores) which is left behind after removal or decomposition of the original particles. Residual hollow honeycomb structures provide a relative index of refraction (ratio of matrix to air) sufficient for selective filters. Variable index liquids or liquid crystals injected into the network alter the ratio and band gap.

Such frequency-sensitive devices may be ideal for optical switching and frequency selective filters in the ultraviolet, visible, or infrared portions of the spectrum, as well as higher efficiency antennae at microwave and millimeter wave frequencies.

Ceramics processing

In the processing of fine ceramics, the irregular particle sizes and shapes in a typical powder often lead to non-uniform packing morphologies that result in packing density variations in the powder compact. Uncontrolled agglomeration of powders due to attractive vander Waals forces can also give rise to in microstructural inhomogeneities. [32] Differential stresses that develop as a result of non-uniform drying shrinkage are directly related to the rate at which the solvent can be removed, and thus highly dependent upon the distribution of porosity. [33] Such stresses have been associated with a plastic-to-brittle transition in consolidated bodies, and can yield to crack propagation in the unfired body if not relieved. [34]

Any fluctuations in packing density in the compact as it is prepared for the kiln are often amplified during the sintering process, yielding inhomogeneous densification.[35] Some pores and other defects associated with density variations have been shown to play a detrimental role in the sintering process by growing and thus limiting end-point densities. Differential stresses arising from inhomogeneous densification have also been shown to result in the propagation of internal cracks, thus becoming the strength-controlling flaws.

Mono-disperse powders of colloidal silica, for example, may therefore be stabilized sufficiently to ensure a high degree of order in the colloidal crystal or polycrystalline colloidal solid which results from aggregation or methods of controlled consolidation.[36]

The degree of order appears to be limited by the time and space allowed for longer-range correlations to be established. Such defective polycrystalline colloidal structures would appear to be the basic elements of submicrometre colloidal materials science, and, therefore, provide the first step in developing a more rigorous understanding of the mechanisms involved in microstructural evolution in inorganic systems such as polycrystalline ceramics.[31]
SEM micrograph of surface of colloidal solid. Structure and morphology consists of ordered domains with both interdomain and intradomain lattice defects.(Amorphous colloidal silica particles of average particle diameter 600 nm).

Self-assembly

Self-assembly is the most common term in use in the modern scientific community to describe the spontaneous aggregation of particles (atoms, molecules, colloids, micelles, etc.) without the influence of any external forces.[14] Large groups of such particles are known to assemble themselves into thermodynamically stable, structurally well-defined arrays, quite reminiscent of one of the 7 crystal systems found in metallurgy and mineralogy (e.g. face-centered cubic, body-centered cubic, etc.). The fundamental difference in equilibrium structure is in the spatial scale of the unit cell (or lattice parameter) in each particular case.

Molecular self-assembly is found widely in biological systems and provides the basis of a wide variety of complex biological structures. This includes an emerging class of mechanically superior biomaterials based on microstructural features and designs found in nature. Thus, self-assembly is also emerging as a new strategy in chemical synthesis and nanotechnology.[13] Molecular crystals, liquid crystals, colloids, micelles, emulsions, phase-separated polymers, thin films and self-assembled monolayers all represent examples of the types of highly ordered structures which are obtained using these techniques. The distinguishing feature of these methods is self-organization.

See also

* Crystal growth
* Crystal structure
* Ceramic engineering
* Nanomaterials
* Nanoparticle
* Nucleation
* Photonic crystal
* Physics of glass
* Sol-gel

References

1. ^ Pieranski, P., Contemp. Phys., Colloidal Crystals, Vol.24, p.25 (1983) doi:10.1080/00107518308227471
2. ^ Sanders, J.V., Structure of Opal, Nature, Vol.204, p.1151, (1964) doi:10.1038/204990a0; Darragh, P.J., et al., Opal, Scientific American, Vol. 234, p. 84, (1976)
3. ^ Luck, W. et al., Ber. Busenges Phys. Chem. , Vol. 67, p.84 (1963)
4. ^ Hiltner, P.A. and Krieger, I.M., Diffraction of Light by Ordered Suspensions, J. Phys. Chem., Vol.73, p.2306 (1969)
5. ^ Langmuir, I., The Role of Attractive and Repulsive Forces in the Formation of Tactoids, Thixotropic Gels, Protein Crystals and Coacervates, J. Chem. Phys., Vol.6, p.873 (1938) doi:10.1063/1.1750183
6. ^ Bernal. J.D. and Fankuchen, I., X-ray and Crystallographic Studies of Plant Virus Preparations J. Gen. Physiol., Vol.25, p.111 (1941)
7. ^ Williams, R.C. and Smith, K., A Crystallizable Insect Virus, Nature (Lond.), Vol. 119, p.4551 (1957) doi:10.1038/179119a0
8. ^ Watson, J.D., Molecular Biology of the Gene, Benjamin, Inc. (1970)
9. ^ Stanley, W.M., Crystalline Form of the Tobacco Mosaic Virus, Am. J. Botany, Vol.24, p.59 (1937); Nobel Lecture: The Isolation and Properties of Crystalline TMV (1946)
10. ^ Murray, C.A. and Grier, D.G., Colloidal Crystals, Amer. Scientist, Vol.83, p.238 (1995) ; Video Microscopy of Monodisperse Colloidal Systems, Ann. Rev. Phys. Chem., Vol.47, p.421 (1996) doi:10.1146/annurev.physchem.47.1.421; Microscopic Dynamics of Freezing in Supercooled Colloidal Fluids, J. Chem. Phys., Vol.100, p.9088 (1994) doi:10.1063/1.466662; (also in Ref. 18-20)
11. ^ Russel, W.B., et al., Eds. Colloidal Dispersions (Cambridge Univ. Press, 1989) [see cover]
12. ^ a b Allman III, R.M., Structural Variations in Colloidal Crystals, M.S. Thesis, UCLA (1983). See Ref.14 in Mangels, J.A. and Messing, G.L., Eds., Forming of Ceramics, Microstructural Control Through Colloidal Consolidation, I.A. Aksay, Advances in Ceramics, Vol.9, p.94, Proc. Amer. Ceramic Soc. (1984)
13. ^ a b Whitesides, G.M., et al., Molecular Self-Assembly and Nanochemistry: A Chemical Strategy for the Synthesis of Nanostructures, Science, Vol. 254, p.1312 (1991)doi:10.1126/science.1962191
14. ^ a b Aksay, I.A., et al., Self-Assembled Ceramics, Ann. Rev. Phys. Chem., Vol. 51, p.601 (2000)
15. ^ Auburt, C., Cannell, D.S., Restructuring of colloidal silica aggregates, Phys. Rev. Lett., Vol.56, p.739 (1986) doi:10.1103/PhysRevLett.56.738
16. ^ Witten, T.A. and Sander, L.M., Diffusion-Limited Aggregation, a Kinetic Critical Phenomenon, Phys. Rev. Lett., Vol.47, p.1400 doi:10.1103/PhysRevLett.47.1400;Diffusion-limited aggregation, Phys. Rev. Vol.B27, p.5686 (1983) doi:10.1103/PhysRevB.27.5686
17. ^ Crandall, R.S., Williams, R.,Gravitational Compression of Crystallized Suspensions of Polystyrene Spheres, Science, Vol.198, p.193 (1977) doi:10.1126/science.198.4314.293
18. ^ Mitaku, S., et al., Studies of Ordered Monodisperse Latexes, Jpn. J. Appl. Phys., Vol.17, p.305 (1978) doi:10.1143/JJAP.17.305 ; Vol.19, p.439 (1980) doi:10.1143/JJAP.17.627
19. ^ Russel, W.B., et al., JCIS, Vol.83, p.163 (1981)
20. ^ Phan, S.E., Russel, W.B., Cheng, Z., Zhu, J., Chaikin, P.M., Dunsmuir, J.H., Ottewill, R.H., Phase transition, equation of state, and limiting shear viscosities of hard sphere dispersions, Phys. Rev. E, Vol. 54, p. 6633 (1996)doi:10.1103/PhysRevE.54.6633
21. ^ Cheng, Z., Russel, W.B., Chaikin, P.M., Controlled growth of hard-sphere colloidal crystals, Nature, Vol. 401, p.893 (1999) doi:10.1038/44785
22. ^ Davis, K.E., Russel, W.B., Glantschnig W.J., Disorder-to-Order Transition in Settling Suspensions of Colloidal Silica: X-ray Measurements, Science, Vol. 245, p.507 (1989) doi:10.1126/science.245.4917.507
23. ^ Cheng, Z., Zhu, J., Russel, W.B., and Chaikin, P.M., Phonons in an Entropic Crystal, Phys. Rev. Lett., Vol. 85, p. 1460 (2000)
24. ^ Penciu, R.S., et al., Phonons in colloidal crystals, Europhys. Lett., Vol. 58, p. 699 (2002)
25. ^ a b Sogami, I., Yoshiyama, T., Phase Transitions, Vol.21, p.171 (1990)
26. ^ Schatzel, K., Adv. Coll. Int. Sci., Vol.46, p.309 (1993) ; [also in ref. 8-10]
27. ^ Ito, K., et al., Phys. Rev., Vol.B41, p.5403 (1990)
28. ^ Yoshida, H. et al., Phys. Rev., Vol.B44, p.435 (1991) ; J. Chem. Soc. Farad. Trans., Vol.87, p.371 (1991)
29. ^ Zhu, J., et al. / STS-73 Space Shuttle Crew, Nature, Vol.387, p.883 (1997)
30. ^ Armstrong, A.J., Mockler, R.C., O'Sullivan, W.J., J. Phys: Cond. Matt., Vol.1, 1707 (1989)
31. ^ a b Allman III, R.M. and Onoda, G.Y., Jr. (IBM T.J. Watson Research Center, 1984)
32. ^ Aksay, I.A., Lange, F.F., Davis, B.I., J. Am. Ceram. Soc., Vol. 66, p.C-190 (1983)
33. ^ Franks, G.V. and Lange, F.F., J. Am. Ceram. Soc., Vol.79, p.3161 (1996)
34. ^ Onoda, G.Y., Jr. and Hench, L.L. Eds., Ceramic Processing Before Firing (Wiley & Sons, New York, 1979)
35. ^ Evans, A.G. and Davidge, R.W., Phil. Mag., Vol.20, p.164 (1969) ; J Mat. Sci., Vol.5, p.314 (1970)
36. ^ Allman III, R.M. in Microstructural Control Through Colloidal Consolidation, Aksay, I.A., Adv. Ceram., Vol. 9, p. 94, Proc. Amer. Ceramic Soc. (Columbus, OH 1984)