Rigidity of colloidal alloys as studied by reflection spectroscopy in sedimentation equilibrium

Rigidities of colloidal alloys of binary mixtures of colloidal silica spheres (CS82; 103 nm in diameter) with larger silica spheres (CS91; 110 nm, CS121; 136 nm and CS161; 184 nm) have been measured by reflection spectroscopy in sedimentation equilibrium. Substitutional-solid-solution-type alloy structures are formed for mixtures of CS82 and CS91 and for CS82 and CS121. A superlattice, probably MgCu₂ type, is formed for CS82 and CS161 mixtures. The rigidities of the colloidal crystals of the single component of the spheres increase as the sphere size increases at the same number density of spheres. The rigidities of the colloidal alloys decrease when a comparatively small number of the larger spheres are mixed with the small spheres at the same total sphere number density. Received: 14 June 2000 Accepted: 3 November 2000     

Colloidal crystals of core-shell type spheres with poly(styrene) core and poly(ethylene oxide) shell

Elastic modulus and crystal growth kinetics have been studied for colloidal crystals of core–shell type colloidal spheres (diameter = 160–200 nm) in aqueous suspension. Crystallization properties of three kinds of spheres, which have poly(styrene) core and poly(ethylene oxide) shell with different oxyethylene chain length (n = 50, 80 and 150), were examined by reflection spectroscopy. The suspensions were deionized exhaustively for more than 1 year using mixed bed of ion-exchange resins. The rigidities of the crystals range from 0.11 to 120 Pa and from 0.56 to 76 Pa for the spheres of n = 50 and 80, respectively, and increase sharply as the sphere volume fraction increase. The g factor, parameter for crystal stability, range from 0.029 to 0.13 and from 0.040 to 0.11 for the spheres of n = 50 and 80, respectively. These g values indicate the formation of stable crystals, and the values were decreased as the sphere volume fraction increased. Two components of crystal growth rate coefficients, fast and slow, were observed in the order from 10⁻³ to 10¹ s⁻¹. This is due to the secondary process in the colloidal crystallization mechanism, corresponding to reorientation from metastable crystals formed in the primary process and/or Ostwald-ripening process. There are no distinct differences in the structural, kinetic and elastic properties among the colloidal crystals of the different core–shell size spheres, nor difference between those of core–shell spheres and silica or poly(styrene) spheres. The results are very reasonably interpreted by the fact that colloidal crystals are formed in a closed container owing to long-range repulsive forces and the Brownian movement of colloidal spheres surrounded by extended electrical double layers, and their formation is not influenced by the rigidity and internal structure of the spheres.     

Giant colloidal crystals of fluorine-containing polymer spheres in exhaustively deionized aqueous suspensions and in the presence of sodium chloride

 Gigantic colloidal single crystals (2–6 mm) are formed for fluorine-containing polymer spheres (120–210 nm in diameter) in exhaustively deionized aqueous suspensions. The spheres used are poly(tetrafluoroethylene) (PTFEA and PTFEB), copolymer of tetrafluoroethylene and perfluorovinylether (PFA) and copolymer of tetrafluoroethylene and perfluoropropylene (PTP). The phase diagrams of these spheres are obtained in the deionized suspensions and also in the presence of sodium chloride for PFA. The critical sphere concentrations of crystal melting (φ _c) for these spheres are around 0.0006 in volume fraction, which are close to, but slightly larger than, those of monodispersed polystyrene spheres (φ _c ≈ 0.00015) and colloidal silica spheres(φ _c = 0.0002–0.0004) reported previously. The crystals are largest when the sphere concentrations are a bit higher than the φ _c value and their size decreases as the sphere concentration increases. Reflection spectra are taken in sedimentation equilibrium as a function of the height from the bottom of the suspension. The static elastic modulus is estimated to be 10.8 and 28.7 Pa for PTFEA and PTP spheres at the sphere concentrations 0.00325 and 0.00322 in volume fraction, respectively. Received: 27 October 1999 Accepted in revised form: 16 November 1999     

Effects of liquid bridge between colloidal spheres and evaporation temperature on fabrication of colloidal multilayers

For the application of colloidal crystal films as "photonic band gap" materials, their domain size and thickness are significant. The substrate withdrawing speed, the colloidal suspension volume fraction, and the colloidal suspension temperature have been studied for the domain size and thickness controls of colloidal crystals in this study. Stable dispersions of monodispersed polystyrene spheres with a diameter of 245 nm were synthesized according to a general emulsion polymerization for colloidal crystal films. By experimental results and the theoretical relationship between the number of layers and other parameters, we could know that the water bridge between colloidal spheres (which is formed by capillary force) influences the number of colloidal crystal layers significantly.     

Colloidal crystals of core–shell-type spheres in deionized aqueous suspension

The structure, crystal growth kinetics and rigidity of colloidal crystals of core–shell-type latex spheres (diameters 280–330 nm) with differences in shell rigidity have been studied in aqueous suspension, mainly by reflection spectroscopy. The suspensions were deionized exhaustively for more than 2 years using mixed-bed ion-exchange resins. The five kinds of core–shell spheres examined form colloidal crystals, where the critical sphere concentrations, _c, of crystallization (or melting) are high and range from 0.01 to 0.06 in volume fraction. Nearest-neighbor intersphere distances in the crystal lattice agree satisfactorily with values calculated from the sphere diameter and concentration. The crystal growth rates are between 0.1 and 0.3 s^–1 and decrease slightly as the sphere concentration increases, indicating that the crystal growth rates are from the secondary process in the colloidal crystallization mechanism, corresponding to reorientation from metastable crystals formed in the primary process and/or Ostwald-ripening process. The rigidities of the crystals range from 2 to 200 Pa, and increase sharply as the sphere concentration increases. The g factor, the parameter for crystal stability, is around 0.02 irrespective of the sphere concentration and/or the kind of core–shell sphere. There are no distinct differences in the structural, kinetic and elastic properties among the colloidal crystals of the different core–shell-type spheres, showing that the internal sphere structure does not affect the properties of the colloidal crystals. The results show that colloidal crystals form in a closed container owing to long-range repulsive forces and the Brownian movement of colloidal spheres surrounded by extended electrical double layers and that their formation is not influenced by the rigidity and internal structure of the spheres.     

Cationic gel crystals of lightly cross-linked poly(2-vinylpyridine) spheres (170∼180 nm in diameter) in the deionized aqueous suspension

Colloidal crystallization of deionized suspensions of the cationic gel spheres of lightly cross-linked poly(2-vinylpyridine), AIBA-P2VP (170～180 nm in diameter) has been studied from the microscopic observation, morphology, phase diagram, and elastic property. Critical concentrations of melting that coexisted with ion-exchange resins were low compared with those without resins and decreased as the degree of cross-linking decreased. The density of a gel sphere in suspension state (ρ), i.e., weight percent of the gel spheres divided by the corresponding volume percent, was between 0.5 and 0.8, and decreased as the degree of cross-linking of the spheres decreased. The ρ values also decreased with decreasing size of gel spheres, which supports the small P2VP gel spheres being softer than the large ones. The closest intersphere distances of the crystals were much longer than the hydrodynamic diameters of the gel spheres especially at low sphere concentrations. Fluctuation parameters evaluated from the rigidities of the crystals of AIBA-P2VP (0.05～0.09) were similar to those of gel crystals of cationic gel spheres of lightly cross-linked poly(2-vinylpyridine) spheres coated with poly(ethylene glycol), 400 nm in diameter, and thermo-sensitive gel spheres of pNIPAm, poly(N-isopropylacrylamide), but larger than those of typical colloidal hard spheres. The stable crystal phase formed beyond the adsorbed monolayer of cationic gel spheres on the surface of the substrate. These experimental findings support important role of the extended electrical double layers around the cationic gel spheres in addition to the excluded volume effect of the sphere themselves on the crystallization.     

Cationic gel crystals and amorphous solids of lightly cross-linked poly(2-vinylpyridine) spheres in the deionized aqueous suspension

Colloidal crystallization and amorphous solidification of deionized suspensions of the polydispersed cationic gel spheres of lightly cross-linked poly(2-vinylpyridine), CAIBA-P2VP (107～113 nm in diameter, ±19～22 nm in dispersity), have been studied from the reflection spectroscopy, morphology, phase diagram, and elastic property. Crystallization takes place even for the polydispersed cationic gel spheres by the significant contribution of the extended electrical double layers formed around the spheres. Critical concentrations of melting coexisted with ion exchange resins were around 0.02 in volume fraction and high compared with those of other cationic and anionic gel crystals examined hitherto. The densities (ρ) of CAIBA-P2VP in suspension state, i.e., weight percent of the gel spheres divided by the corresponding volume percent, was around 0.3. The ρ values decreased sharply with decreasing size of P2VP gel spheres, which supports the small gel spheres containing much water inside and being softer than the large ones. The closest intersphere distances of the crystals and/or amorphous solids were much longer than the hydrodynamic diameters of the gel spheres especially at low sphere concentrations. Fluctuation parameters (b) evaluated from the rigidities of CAIBA-P2VP (0.15～0.28) were large compared with those of gel crystals of large-sized P2VP-based cationic gel spheres, anionic thermosensitive gel spheres of poly(N-isopropylacrylamide) (0.05～0.09) and further much larger than those of typical colloidal hard spheres (around 0.03). The dispersity in sphere size played an important role for distinguishing crystal and amorphous solid. Importance of the extended electrical double layers around the cationic gel spheres is supported in addition to the excluded volume effect of the sphere themselves on the crystallization and/or solidification.     

Colloidal crystallization of poly(n-butyl acrylate) spheres in deionized aqueous suspension and the melting during dryness

Colloidal crystallization of poly(n-butyl acrylate) spheres (ammonium persulfate-poly(n-butyl acrylate) (APS-PBA), 320?±?50 nm in diameter) was studied in deionized aqueous suspension. Coexistence of the crystal and distorted crystal structures was observed by the reflection spectroscopy. The critical concentrations of melting were ca. 0.01 and 0.03 in volume fraction in the presence of ion-exchange resins and in their absence, respectively. Crystal structures melted away during dryness by fusion of each spheres on the substrates, i.e., cover glass, watch glass, and Petri glass dish. Thickness profiles of the dried film changed sharply from the broad ring to the round hill as sphere concentration increased. The sharpness parameter S was evaluated from the ratio of the film size (diameter) against the full width at half maximum in the thickness profiles of the ring and/or the round hill. The S values decreased sharply from 30 to 1.2 as initial volume fraction of the spheres increased from 0.0005 to 0.1. The S values were significantly low compared with those of typical colloidal spheres, which supports the aggregate and/or fusion of the spheres resulting in their low convectional flow during dryness. The round hill profile at the high sphere concentration also supports that the fusion takes place easier during dryness. Microscopic observation of the dried film supports the formation of the homogeneous fused structures. It was clarified that colloidal crystallization of APS-PBA spheres takes place by the extended electrical double layers around the spheres like typical colloidal crystals of hard spheres. However, APS-PBA spheres are not so stable by the fusion especially at the high sphere concentrations and on the substrates.     

Rigidity of colloidal crystals of silica spheres modified with polymers on their surfaces in organic solvents

Rigidity (G) of colloidal crystals in organic solvents of acetonitrile and nitrobenzene has been measured by reflection spectroscopy in sedimentation equilibrium. The colloidal spheres used are the silica spheres (136 nm in diameter) modified on their surfaces with polymers, poly(maleic anhydride-co-styrene) [P(MA-ST)], poly(methyl methacrylate) (PMMA), or polystyrene (PST). Log G increases linearly with the slope of unity as log N (number density of colloidal spheres) increases. The mean values of the b-factor, which is the fluctuation parameter in crystal lattices and should be smaller than 0.1 according to the Lindeman's rule, are 0.045±0.003, 0.039±0.007, and 0.038±0.003 for P(MA-ST)/SiO₂, PMMA/SiO₂, and PST/SiO₂, respectively. These values are larger than that of colloidal crystals of mother silica spheres in the deionized aqueous suspension, 0.028. These results support the important role of the excluded volume effects from the polymer layers formed around the silica surfaces. However, contribution of the excluded volume effects from the electrical double layers formed around the spheres in the organic solvents is also effective in the colloidal crystallization. Electronic Publication     

Convectional, sedimentation, and drying dissipative patterns of colloidal silica (183 nm in diameter) suspensions in a glass dish and a watch glass

Convectional, sedimentation, and drying dissipative structural patterns formed during the course of drying aqueous colloidal crystals of silica spheres (183 nm in diameter) have been studied in a glass dish and a watch glass. Spoke-like convectional patterns were observed in a watch glass. The broad ring sedimentation patterns formed especially in a glass dish within 30–40 min in suspension state by the convectional flow of water and colloidal spheres. The macroscopic broad ring drying patterns formed both in a glass dish and a watch glass. The ratio of the broad ring size in a glass dish against the initial size of suspension, i.e., inner diameter of the glass dish, d _f/d _i, in this work, were compared with previous work of other silica spheres having sizes of 305 and 560 nm and 1.2 μm in diameter. The d _f/d _i values in a glass dish increased as sphere concentration increased, but were rather insensitive to colloidal size. The d _f/d _i values on a watch glass also increased as sphere concentration increased, and further increased as sphere size decreased. Segregation effect by sphere size in a watch glass takes place by the balancing between the upward convectional flow of spheres in the lower layers of the liquid and the downward sedimentation of spheres. Colorful microscopic drying patterns formed both in a glass dish and a watch glass.     

Colloidal crystals of cationic spheres

Colloidal single crystals of cationic polymer spheres (198–250 nm in diameter) in deionized aqueous dispersions were formed for the first time. The spheres used were poly(styrene-co-methacryloyloxyphenyldimethylsulfonium) cations. These cations are unstable in deionized suspensions with mixed beds of cation-exchange and anion-exchange resins. This was clarified by reflection spectroscopy, pH, conductance and -potential measurements for 250 days after suspension preparation. Colloidal crystals formed over a period of 24 h for the deionized suspensions at sphere concentrations higher than 0.09 in volume fraction. The nearest-neighbor intersphere distances coincide satisfactorily with the calculated values using the diameter and the concentration of the spheres. Alloy crystals formed from binary mixtures of the cationic polymer spheres and the anionic silica spheres when the ratio of the volume fraction of cationic spheres against the sum of the both cationic and anionic spheres was smaller than 0.3.     

Suspension viscosity of colloidal crystals and liquids in exhaustively deionized aqueous suspensions coexisting with ion-exchange resins

 Viscosities of exhaustively deionized aqueous suspensions of colloidal silica spheres are measured with coexisting ion-exchange resins using an Ubbelohde-type viscometer. The reduced viscosities of small silica spheres (56.3 nm in diameter) with and without resins decrease as the sphere concentration increases. However, the former are larger than the latter especially at low sphere concentrations. The reduced viscosities of other silica spheres, 81.2, 103, 110 and 136 nm in diameter, with resins decrease as the sphere concentration increases, whereas those without resins increase especially at low sphere concentrations. The significant effect of the extent of deionization upon the viscometric properties supports the important role of the extended electrical double layers formed around the colloidal spheres. Received: 28 October 1999 Accepted: 24 December 1999     

Effects of particle volume fraction on distortion of particle-arrayed structure during immobilization of colloidal crystals formed by poly(methyl methacrylate)-grafted silica in acetonitrile

Changes of particle array structure with particle volume fraction during immobilization of colloidal crystals, formed by poly(methyl methacrylate)-grafted silica in acetonitrile, were investigated. Immobilization of colloidal crystals formed in acetonitrile was carried out by two-step photo-radical copolymerization of methyl methacrylate and ethylene dimethacrylate to make organogel, followed by solidification after exchanging the solvent with methyl methacrylate. Crystallite size in colloidal crystals formed in acetonitrile was mostly unchanged with particle volume fraction in the range of 0.11–0.18, while the size and number of single crystals decreased during gelation. Disordering in particle array in immobilized colloidal crystals in gel and poly(methyl methacrylate) matrix was observed to decrease with increasing particle volume fraction less than 0.18 due to strong electrostatic repulsion between particles.     

Colloidal crystallization of thermo-sensitive gel spheres of poly (<Emphasis Type="Italic">N</Emphasis>-isopropyl acrylamide). Influence of gel size

Influence of the gel size on the morphology, phase diagram, and reflection spectroscopy of the colloidal crystals of thermo-sensitive gel spheres, poly (N-isopropylacrylamide) (pNIPAm), was discussed by adding the data of two gel samples of pNIPAm(400–5) and pNIPAm(600–5) of 412 nm (at 25 °C) and 220 nm (at 45 °C) and of 517 nm (at 20 °C) and 294 nm (at 45 °C), respectively. Colloidal single crystals formed, but not so large compared with the giant crystals of small pNIPAm gels reported previously. The suspensions even with ion-exchange resins were turbid and hard to observe the single crystals clearly with the naked eyes as gel size increased. The critical concentration of melting decreased sharply as the suspensions were deionized with coexistence of the mixtures of cation- and anion-exchange resins. The critical concentration increased as the gel size increased and/or dispersion temperature increased. Density of the gel spheres increased as their size increased. These results demonstrated that the colloidal crystallization takes place by the extended electrical double layers formed around the gel spheres in addition of the excluded volume effect of the gels. Contribution of the electrical double layers on the crystallization increased sharply as temperature increased and gel concentration decreased, respectively. The contribution also increased slightly as sphere size increased, when comparison was made at the same gel concentration in wt.%. The present work clarified that the colloidal interfaces, which are inevitable for the formation of the electrical double layers, are formed between the water phase and gel spheres, though the gel spheres contain a lot of water molecules at the inner sphere region.     

Kinetic analyses of colloidal crystallization in shear flow

Colloidal crystallization kinetics is studied in the shear flow of a suspension of colloidal silica spheres (110 nm in diameter), using a continuously-circulating type of stopped flow cell system. The crystallization rate from a suspension containing a small amount of nuclei and/or single crystals is high compared with that from a suspension containing no nuclei and/or single crystals. Crystal growth takes place at shear rates smaller than 3.4 s^–1 and at sphere concentrations higher than a volume fraction of 0.004.     

Sedimentation and drying dissipative patterns of binary suspensions of colloidal silica spheres having different sizes

The sedimentation and drying dissipative structural patterns were formed during the course of drying binary mixtures among colloidal silica spheres of 183 nm, 305 nm, and 1.205 μm in diameter in aqueous suspension on a watch glass, a glass dish, and a cover glass, respectively. The broad ring-like sedimentation patterns were formed within several hours in suspension state for all the substrates used. Colorful macroscopic broad ring-like drying patterns were formed for the three substrates. In a watch glass, macroscopic drying patterns were composed of the outer and inner layers of small and large spheres, respectively. The two colored layers were ascribed to the Bragg diffractions of light by the dried colloidal crystals of the corresponding spheres. The width ratio of the layers changed in proportion to the mixing ratio of each spheres. In a glass dish, wave-like macroscopic drying patterns were observed in the intermediate areas between the outside edges of the broad ring and the inner wall of the cell. On a cover glass, the sphere mixing ratios were analyzed from the widths of the drying broad rings of the small spheres at the outside edge. High and distinct broad rings of small spheres and the low and vague broad one formed at the outer edges and in the inner area, respectively. Drying dissipative pattern was clarified to be one of the novel analysis techniques of colloidal size in binary colloidal mixtures.     

Drying dissipative structures of the deionized aqueous suspensions of colloidal silica spheres ranging from 29 nm to 1 μm in diameter

Macroscopic and microscopic dissipative structural patterns formed in the course of drying a series of the colloidal silica spheres ranging from 29 nm to 1 m in diameter have been observed in the aqueous deionized suspension on a cover glass. The broad ring patterns of the hill accumulated with the silica spheres are formed around the outside edges in the macroscopic scale for all spheres examined. The spoke-like cracks are also observed in the macroscopic scale and their number decreases sharply as sphere size increases. The pattern area and the time for the dryness have been discussed as a function of sphere size and concentration. The convection flow of water accompanied with that of the silica spheres and interactions among the silica spheres and substrate are important for the macroscopic pattern formation. The microscopic fractal structures of the wave-like patterns and branched strings are formed. Their fractal dimensions are determined. Microscopic patterns form in the narrow range of sphere sizes and concentrations and are determined mainly by the electrostatic and polar interactions between the spheres and/or between the sphere and substrate in the course of solidification.     

Self-ordering of colloidal particles in shallow nanoscale surface corrugations

The influence of nanoscale out-of-plane roughness on the ordering of submicron spheres during evaporative deposition from colloidal suspension was examined using shallow corrugated substrates possessing optical wavelengths and nanoscale amplitude. Under conditions in which spheres were embedded in a liquid layer with thickness on the order of the sphere diameter, it was observed that the spheres overwhelmingly deposited in the valleys of the surface corrugations rather than on their peaks. This behavior persisted to surprisingly shallow corrugation amplitudes, sometimes 100 times smaller than the sphere diameter. An analysis of the capillary forces on the spheres explains this behavior and also yields a critical corrugation amplitude below which a substrate will appear "flat" to depositing spheres. The observation that substrate features significantly smaller than the sphere diameter can influence deposition morphology may lead to simple methods to create large domains of order in colloidal crystals.     

Convectional,sedimentation, and drying dissipative patterns of colloidal crystals of poly (methyl methacrylate) spheres on a cover glass

Direct observation of the convectional dissipative patterns was successful during the course of dryness of colloidal crystals of poly (methyl methacrylate) spheres on a cover glass. Formation processes of the convectional patterns of spoke-like lines were observed as a function of sphere size and also sphere concentration. During dryness of the suspensions, the brilliant iridescent colors changed beautifully. Macro- and microscopic drying patterns and thickness profiles of the dried film were observed. Sharp broad rings were observed especially at low sphere concentrations. The water evaporation accompanied with the convectional flow of water and the colloidal spheres played an important role for these dissipative structure formation.     

Fabrication of spherical colloidal crystals using electrospray

We demonstrated the use of electrohydrodynamic atomization to prepare uniform-sized emulsion droplets in which equal spheres of silica or polystyrene were dispersed. The size of the emulsion droplets was easily controlled by the electric field strength and the flow rate, independently of the diameter of the nozzles. During the evaporation of solvent in the droplets, spherical colloidal crystals were formed by self-assembly of the monodisperse colloidal spheres. The diameter of the spherical colloidal crystals was in the range of 10-40 microm. Depending on the stability of colloidal particles, the morphology of the self-assembled structure was varied. In particular, silica spheres in ethanol droplets were self-assembled into compactly packed silica colloidal crystals in spherical shapes, whereas polystyrene latex spheres in toluene droplets self-assembled into spherical colloidal crystal shells with hollow cores. The silica colloidal assemblies reflected diffraction colors according to the three-dimensionally ordered arrangement of silica spheres.