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 thermo-sensitive gel spheres of poly (N-isopropyl acrylamide). Influence of degree of cross-linking of the gels

Morphology, phase diagram, and reflection spectroscopy of the colloidal crystals of thermo-sensitive gel spheres, poly (N-isopropylacrylamide) having degrees of cross-linking 10 and 2?mol.% (pNIPAm(200?C10) and pNIPAm(200?C2)) were studied. Giant colloidal single crystals formed at very low gel concentrations. Critical concentrations of melting increased as the degree of cross-linking decreased in the range from 10 to 0.5?mol.% and/or suspension temperature increased from 20 to 45?°C. The critical concentration decreased sharply as the suspensions were deionized with coexistence of the mixtures of cation- and anion-exchange resins. Density of a gel sphere (gel concentration in weight percent divided by that in volume percent) increased sharply as the degree of cross-linking and/or temperature 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. Most of the researchers including the authors have believed that the crystallization of the gel spheres takes place by the excluded-volume effect. However, the present work clarified that the colloidal interfaces, which are inevitable for the formation of the electrical double layers, are formed firmly between the water phase and gel spheres, though the gel spheres contain a lot of water molecules in the sphere region.     

Colloidal crystallization of thermosensitive gel spheres of poly(<Emphasis Type="Italic">N</Emphasis>-isopropylacrylamide) with low degree of cross-linking

Morphology, phase diagram, and reflection spectroscopy of the colloidal crystals of thermosensitive gel spheres, poly(N-isopropylacrylamide) ((200–0.5), 318 and 116 nm in the hydrodynamic diameter at 25°C and 45°C, and 0.5% in the degree of cross-linking) were studied. Giant colloidal single crystals formed at very low gel concentrations. Densities of the gel spheres were 0.030 and 0.61 at 25°C and 45°C, respectively. Critical concentration of melting of gel spheres (0.8 wt.% without ion-exchange resins) decreased sharply to 0.015 wt.% at 25°C as the gel suspension was deionized exhaustively with coexistence of the mixtures of cation and anion exchange resins. These results demonstrate 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. Extent of the contribution of the electrical double layers on the crystallization increased sharply when the degree of cross-linking increased, the gel spheres shrank, and/or the density of the gel spheres increased.     

Rigidity of the crystals of thermo-sensitive gel spheres of poly (N-isopropyl acrylamide) in the deionized aqueous media as studied by the reflection spectroscopy in the sedimentation equilibrium

Reflection spectroscopy of deionized suspensions of the thermo-sensitive gels of poly (N-isopropylacrylamide) with various degrees of cross-linking were made in the sedimentation equilibrium at 20 °C. Rigidity of the crystals increased as sphere concentration increased and increased slightly as the degree of the cross-linking of the gel spheres increased. The fluctuation parameters of the gel crystals were between 0.05 and 0.07 and slightly larger than those of typical hard-sphere systems. These experimental results emphasize that the gel crystals are soft compared with those of typical hard-sphere systems and role of the extended electrical double layers for the crystallization of gel spheres is important but weak compared with that of hard colloidal spheres.     

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

Morphology, phase diagram, and reflection spectroscopy of the colloidal crystals of thermo-sensitive gel spheres, poly (N-isopropylacrylamide) (224 nm in the hydrodynamic diameter at 25 °C) were studied. Giant colloidal single crystals formed at very low gel concentrations. Critical concentration of melting of gel spheres (0.8 wt.% without ion-exchange resins) decreased sharply to 0.01 wt.% as the gel suspension was deionized exhaustively with coexistence of the mixtures of cation- and anion-exchange resins and increased substantially as concentration of sodium chloride increased. These studies 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. Most of the researchers including the authors have believed that the crystallization of the gel spheres takes place by the excluded-volume effect, in other words, by the hard-sphere model, exclusively. However, the present work clarified that the colloidal interfaces, which are inevitable for the formation of the electrical double layers, are formed firmly between the water phase and gel spheres, though the gel spheres contain a lot of water molecules in the inner the sphere region.     

Kinetic studies of colloidal crystallization of thermo-sensitive gel spheres of poly(N-isopropylacrylamide)

Crystal growth rate coefficients, k of the colloidal crystallization of thermo-sensitive gel spheres of poly(N-isopropylacrylamide) were measured from the time-resolved reflection spectroscopy mainly by the inverted mixing method in the deionized state. Crystallization of colloidal silica spheres were also measured for comparison. The k values of gel and silica systems increased sharply as the sphere concentration and suspension temperature increased. The k values of gel system were insensitive to the degree of cross-linking in the range from 10 to 2?mol% of cross-linker against amount of the monomer in mole and decreased sharply when the degree of cross-linking decreased further to 0.5?%. The k values increased as gel size increased. The k values of gel systems at 20?°C were small and observed only at the very high sphere concentration in volume fraction, whereas those at 45?°C were high but smaller than those of silica systems. Induction time (t _i) after which crystallization starts, increased as the degree of cross-linking increased and/or the gel size decreased at any temperatures, when comparison was made at the same gel concentration. The t _i values at 45?°C were high and decreased sharply with increasing sphere concentration, whereas those at 20?°C were high only at the very high sphere concentrations. Significant difference in the k and t _i values between the soft gels and hard silica spheres was clarified. These kinetic results support that the electrical double layers play an important role for the gel crystallization in addition to the excluded volume of gel spheres. It is deduced further that the electrical double layers of the gel system form from the vague interfaces (between soft gel and water phases) compared with those of typical colloidal hard sphere system.     

Drying dissipative structures of cationic gel spheres of lightly cross-linked poly(2-vinylpyridine) in deionized aqueous suspension

Drying dissipative patterns of cationic gel crystals of lightly cross-linked poly(2-vinylpyridine) spheres (CAIBA-P2VP(0.1), CAIBA-P2VP(0.5), and CAIBA-P2VP(1), 107?~?113 nm in diameter and 0.1, 0.5, and 1 in degrees of cross-linking) were observed on a cover glass, a watch glass, and a Petri glass dish. Convectional spoke line and cluster patterns were recognized with the naked eyes, which supports that these poly(2-vinylpyridine) gel spheres aggregate temporarily and reversibly during the course of drying. Two kinds of broad rings were observed at the outside edge and inner region in the macroscopic drying pattern. The size of the inner rings decreased with gel concentration. Formation of similar-sized aggregates (or agglomerates) and their ordered arrays ((a) ordered ring, (b) spoke lines, (c) net structures, and (d) lattice structures) were observed, though the arrays were not so complete compared with those of large-sized analogous gel spheres. One of the main causes of the incomplete ordering of the aggregates is the rather high polydispersities in the sphere size. The ordering of similar-sized aggregates is common among the gel spheres including anionic poly(N-isopropylacrylamide) and cationic poly(2-vinylpyridine). Size effect of cationic gel spheres on the ordering of the agglomerates was clarified definitely in this work. The role of the convectional flow and the electrical double layers around the agglomerates and their interaction with the substrates during drying was also clarified to be very important for the drying pattern formation.     

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.     

Crystal structure of thermosensitive gel spheres of poly(N-isopropylacrylamide) in the deionized aqueous suspension as studied by the static light-scattering measurements

Static light-scattering measurements of deionized suspensions of the thermosensitive gels of poly(N-isopropylacrylamide) with various degrees of cross-linking and sizes were made at 20 and 40 °C. Sharp scattering peaks are observed in the scattering curve, and they were attributed to the face-centered cubic (fcc) and/or body-centered cubic lattices (bcc) in the distribution of gel spheres. The fcc and bcc crystal structures formed in the stable and unstable conditions, respectively, i.e., the former formed more favorably at high sphere concentrations and/or low temperatures. The closest intersphere distances were much longer than the hydrodynamic diameters of the gel spheres especially at low sphere concentrations. These experimental results emphasize the important role of the extended electrical double layers in the crystallization of gel spheres, though the contribution of the double layers in gel systems is weak compared with that in the typical colloidal spheres.     

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.     

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.     

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.     

Drying dissipative structures of cationic gel spheres of lightly cross-linked poly(2-vinyl pyridine) (170 ∼ 180 nm in diameter) in the deionized aqueous suspension

Drying dissipative patterns of cationic gel crystals of lightly cross-linked poly(2-vinyl pyridine) spheres (AIBA-P2VP, 170?～?180 nm in diameter) were observed on a cover glass, a watch glass, and a Petri glass dish. Convectional patterns were recognized with the naked eyes. Two kinds of the broad rings were observed at the outside edge and inner region in the macroscopic drying pattern, and their size at the inner regions first decreased and then turned to increase as gel concentration decreased. Formation of the similar-sized aggregates, i.e., hierarchical aggregation and their ordered arrays were observed. This work supported strongly the formation of the microscopic drying structures of (a) ordered rings, (b) flickering ordered spoke-lines, (c) net structure, and (d) lattice-like ordered structures of the aggregated particles. The ordering of the similar-sized aggregates of the cationic gel spheres (AIBA-P2VP) in this work is similar to that of the large cationic gel spheres of poly(2-vinyl pyridine) (385?～?400 nm in diameter) and further to that of the anionic thermosensitive gel spheres of poly(N-isopropyl acrylamide). Role of the electrical double layers around the aggregates and their interaction with the substrates during dryness are important for the ordering. The microscopic drying patterns of gel spheres were different from those of linear-type polymers and also from typical colloidal hard spheres, though the macroscopic patterns such as broad ring formation were similar to each other.     

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.     

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     

Colloidal crystals formed by aqueous suspensions of monodispersed silica, polystyrene, and poly(methyl methacrylate) colloidal spheres

Colloidal crystals consisted of silica, polystyrene, and poly(methyl methacrylate) monodispersed suspensions; deionized sufficiently in water at the same condition; were formed; and their properties were compared changing sphere diameter and volume fraction systematically. The size of these colloidal crystals was maximized at their critical sphere concentration irrespective of their sphere size. The Bragg peak wavelengths of these colloidal crystals were uniquely determined only by the sphere diameter and volume fraction for all kinds of colloidal spheres used in this work. The larger the sphere volume fraction, the larger the crystal growth rates, and there were no significant differences among the colloidal spheres. The rigidity of colloidal crystals increased in proportion to the number density of spheres. Consequently, the crystallization mechanism and properties of colloidal crystals formed by these spheres are not dependent on the kind of spheres, but they are dependent only on the sphere diameter and number density.     

Kinetic Analyses of Colloidal Crystallization in a Wide Range of Sphere Concentrations as Studied by Reflection Spectroscopy

The nucleation and growth rates in the colloidal crystallization of silica spheres (103 nm in diameter) from 0.006 to 0.04 in volume fraction (straight phi) have been measured by reflection spectroscopy. Kinetics of the crystallization has been discussed in a wide sphere concentration range (from straight phi=0.0005 to straight phi=0.04) using the data of this work and the previous work (110 nm in diameter) in exhaustively deionized aqueous suspensions. The induction period for nucleation decreases sharply as the sphere concentration increases. The nucleation rate increases substantially from 1x10(-3) to 1x10(7) mm(-3) s(-1) when straight phi increases from 0.0005 to 0.04. The crystal growth process consists of the fast growing step toward metastable crystals (rate v(1)) and slow growth accompanied with the reorientation toward stable ones (rate v(2)). The v(1) values increase first from 5 to 20 μm/s and then turn back to 5 μm/s after passing a maximum. v(1) above straight phi=0.01 remains at 5 μm/s and is insensitive to sphere concentration. The slow step is observed in the high-sphere concentrations only, and v(2) decreases sharply from 3 μm/s to 0.7 nm/s when sphere concentration increases from 0.004 to 0.04 in volume fraction. Importance of the electrostatic intersphere repulsion by overlapping of the electrical double layers and the cooperative and synchronized fluctuation of colloidal spheres in the crystallization processes are supported strongly. Copyright 2000 Academic Press.     

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.     

Phase diagram of alloy crystal in the exhaustively deionized suspensions of binary mixtures of colloidal spheres

Phase diagrams of liquidlike, alloy crystal-like and amorphous solid-like(AS) structures have been obtained for the exhaustively deionized aqueous suspensions of the binary mixtures of polystyrene or silica spheres. Diameter, polydispersity index (standard deviation of diameter divided by the mean diameter) and size ratio of the binary spheres (diameter of small sphere divided by that of large one) range from 85 to 136 nm, 0.07 to 0.26 and 0.76 to 0.93, respectively. Close-up color photographs of the alloy crystals are taken and the crystal structure has been analysed from reflection spectroscopy. Most of the alloy crystals aresubstitutional solid-solution (sss) type and body-contered cubic lattice structure. Formation of the alloy crystals is attributed to the important role of the expanded electrical double layers in the deionized condition and increase toward unity in the effective size ratio, which is the effective diameter of small sphere including double layer divided by that of large sphere AS structure is formed at the rather high concentrations of two spheres, where the thickness of the electrical double layer is thin and the effective size rado is comparatively small.